An approach to statistical inference uses bootstrapping to solve problems where the variance is in closed analytic form. Bootstrapping is implemented by creating a number of resamples of the observed sample data set equal in size; obtained by random sampling with replacement from the original dataset.
The military and many other government and private organizations have the need to evaluate ratio mean measurements to help them make informed life cycle management decisions. FIG. 1 is an illustration of a sample ratio mean. A ratio mean is the ratio of the means of two random variables, X and Y, whose corresponding terms are paired. The pairs are assumed to be independent. In FIG. 1, the correlation between X & Y may be positive, negative or zero. The X & Y in FIG. 1 are considered independent and identically distributed (i.i.d.), with some unknown distribution.
For example, the Army tracks and evaluates the performance of many weapon systems using ratio mean metrics, such as the maintenance ratio (MR). A MR estimate
  (                    M        ^            ⁢      R        =                            ∑                      j            =            1                    n                ⁢                  man          ⁢                      -                    ⁢                      hours            j                                                ∑                      j            =            1                    n                ⁢                  miles          j                      )is based on a random sample (without replacement) of n vehicles from a finite population, where the pair (man-hours and miles) are associated with each vehicle.
Since it is inefficient to track every vehicle in an inventory of vehicles, ratio mean performance metrics are tracked for a sample of vehicles over a given time period. The entire population performance is inferred based on a sample of vehicles using approximate confidence intervals (CI) for ratio means. There is need to develop an efficient methodology that provides for the effective use of confidence intervals. Generally speaking, the documented standard error (SE) estimate for a ratio mean (accounts for variation in both variables and correlation) is not dependable for samples under 30 or larger samples with increased variation in both variables. Therefore, another approach is needed.